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Modern Maths

Quant · 4 chapters

Set Theory and Venn Diagrams

22 lessons · 62 questions · 14 PYQs

  • Both neither · Min max both · Percent range both · Only a only b · Venn linear system · Min max with extra condition

  • Inclusion exclusion three · Exactly one two three · Max all three · Min all three · Max liking multiple · Divisibility counting venn · Venn region reading

  • Power set cardinality · Nested power sets · Set builder counting · Cardinality in AP · Subset counting with condition · Set operations identities

Open Set Theory and Venn Diagrams

Permutations and Combinations

62 lessons · 75 questions · 28 PYQs

  • Digits with conditions · Divisible by 5 from set · Greater than threshold · Digit sum condition · Binary digit numbers · Repetition vs no repetition · Divisibility by 3 or 4 · Sum of numbers formed · Monotone digits

  • Arrangements12 lessons

    Words with restrictions · Vowels together separated · Circular with constraints · Seating not adjacent · Rank of word · Identical objects permutations · Block arrangement · Relative order · Derangements · Signals any number · Alternate seating

  • Selections12 lessons

    Committee with inclusion exclusion · At least one of type · Indistinguishable selection · Ncx valid values · Subsets with product condition · Selection from groups · Particular included excluded · Total selections 2n · Select then arrange · NPR NCR equations · Basic combinations

  • Non negative integer solutions · Positive solutions bounded · Distinct into identical boxes · Identical into distinct with caps · Inequality constrained distribution · Distinct into distinct · Identical into identical · Coin combinations · Ordered factorisations · Grouping distinct items

  • Triangles from collinear points · Lines from points · Rectangles from parallel lines · Lattice paths · Staircase steps · Chessboard rooks · Diagonals of polygon · Squares in grid · Intersection points · Polygon triangles

  • Round robin total · Round robin with withdrawal · Knockout matches · Min teams for match count · Handshakes gifts

Open Permutations and Combinations

Probability

34 lessons · 65 questions · 17 PYQs

  • Dice two · Cards · Balls without replacement · Digit divisibility · Three digit number conditions · At least one · Dice three sum · Position symmetry · Selection probability · Odds conversion

  • Bayes truthful reporter · Conditional on sum · Conditional cards · Independent events neither · Total probability bayes · Contradiction independent

  • Alternating shooters · Min trials for threshold · Geometric trials · Binomial exactly k · Independent solvers

  • Factor of power multiple · Perfect square factor · Singular matrix from digits · Divisor property · Unit digit probability

  • Seating separation · Circular seating · Word arrangement probability

Open Probability

Statistics

13 lessons · 67 questions · 7 PYQs

  • Mean median mode basic · Median from grouped counts · Median mean relation · Max min under median · Mean of combined groups · Expected value stratified · Median table constraints · Corrected observation

  • Range · Variance sd basic · Effect of shift scale

Open Statistics